Eigenstate assignments and the quantum-classical correspondence for highly-excited vibrational states of the Baggot H2O Hamiltonian

In this paper we study the classical and quantum mechanics of the 3-mode Baggot vibrational Hamiltonian for H2O. Our aim is to classify and assign highly-excited quantum states based upon a knowledge of the classical phase space structure. In particular, we employ a classical template formed by the primary resonance channels in action space, as determined by Chirikov resonance analysis. More detailed analysis determining the exact periodic orbits and their bifurcations and families of resonant Il-tori for the Baggot Hamiltonian confirms the essential correctness of the Chirikov picture. It is emphasized that the primary periodic orbits alone do not define a suitable phase space skeleton; it is important to consider higher dimensional invariant structures, such as 2-tori and 3-tori. Examining the manifold of quantum states for a given superpolyad number P = n(1)+n(2)+n(b)/2 reveals sequences of eigenstates that progress along the classical resonance zones. These sequences provide insight into the nature of strongly mixed states found in the vicinity of the resonance junction. To further explore the classical-quantum correspondence, we have also computed eigenstate Husimi phase space distribution functions and inverse participation ratios. It is thereby possible to provide dynamically based assignments for many states in the manifold of states with superpolyad number P=16. (C) 1997 American Institute of Physics.